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Exploring the Structure of the Pion

Exploring the Structure of the Pion. Paul E. Reimer Physics Division Argonne National Laboratory 14 October 2010 Why are we interested in the pion? What do we know about the pion? What do we expect? (Dyson- Schwiner equations and the high- x p region). What does the data tell us?

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Exploring the Structure of the Pion

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  1. Exploring the Structure of the Pion Paul E. Reimer Physics Division Argonne National Laboratory 14 October 2010 Why are we interested in the pion? What do we know about the pion? What do we expect? (Dyson-Schwiner equations and the high-xp region). What does the data tell us? Work done with R. Holt and K. Wijesooriya Aicher, Schäfer and Vogelsang, arXiv:1009.2481 This work is supported in part by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC02-06CH11357.

  2. Why are should you be interested in the pion? • Meson Cloud in the nucleon • Sullivan process in DIS • |p = |p0 + α |Nπ+ β|Δπ+ . . . • Chiral Quark • Interaction between Goldstone Bosons and valence quarks • |ui!|d+i and |di!|u-i • Explains quark asymmetry in nucleon sea. Perturbative sea apparently dilutes meson cloud effects at large-x Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  3. Why are should you be interested in the pion? • Explains quark asymmetry in nucleon sea. • Key role in nuclear binding and structure (maybe?). Alde et al (Fermilab E772) Phys. Rev. Lett. 64 2479 (1990) Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  4. Why are should you be interested in the pion? • Explains quark asymmetry in nucleon sea. • Key role in nuclear binding and structure (maybe?). Pion parton distributions play a role in nucleon and nuclear parton distributions Note: QCD tells us how the parton distributions evolve, once we know them, but not what they are. • Simple quark-antiquark system (valence). • Should have an easy theoretical interpretation. • What about mass—constituent quark mass ≈300 MeV each? • QCD’s Goldstone Boson How do we treat 3 and 4 in a unified way? Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  5. Models of the Pion • Nambu and Jona-Lasinio Model: • R. Davidson, E. Arriola, PLB (1995) • J.T. Londerganet al. PLB (1994). • T. Shigetaniet al. PLB (1993). • Dyson Schwinger Equation: • M. Hecht et al. PRD (2001). • ChiralQuark Model: • K. Suzuki, W. Weise, NPA (1998). • D. Arndt, M. Savage, nucl-th (2001) • Light-front constituent quark models: • Gerry Miller, et al. (too many to list). • Instanton Model: • A. Dorokhov, L. Tomio, PRD (2000) • QCD Sum Rule Calculations • A. Bakulevet al. PLB (2001). • Lattice Gauge • C. Best et al. PRD (1997). At some base q0 NJL: xq(x)/ (1-x)bb = 1 pQCD: xq(x)/ (1-x)bb = 2 DSE: xq(x)/ (1-x)bb¼ 1.9 Evolution to experimental Q increases b. Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  6. Experimental Tools for π structure • Deeply Inelastic Scattering: “pion targets are not abundant” Hecht • DIS on virtual pions: ep→eNx HERA data [ZEUS, NPB637 3 (2002)] Possible JLab and EIC. • Low-x data (Different Workshop?) Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  7. Experimental Tools for π structure • Deeply Inelastic Scattering: • “pion targets are not abundant” Hecht • DIS on virtual pions: • ep→eNx HERA data [ZEUS, NPB637 3 (2002)] • Possible JLab and EIC. • Low-x data (Different Workshop?) • Direct photos in πp interactions • Sensitive to gluon distributions. • [CERN WA 70, Z. Phys. C37 535 (1988)] • Assume parameterization • SMRS, PRD45 2349 (1992) Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  8. Experimental Tools for π structure • Deeply Inelastic Scattering: “pion targets are not abundant” Hecht • DIS on virtual pions: ep→eNx HERA data [ZEUS, NPB637 3 (2002)] Possible JLab and EIC. • Low-x data (Different Workshop?) • Direct photos in πp interactions • Sensitive to gluon distributions. • [CERN WA 70, Z. Phys. C37 535 (1988)] • Drell-YanπA Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  9. xtarget xbeam Drell-Yan cross section Detector acceptance chooses xtarget and xbeam. • Fixed target, dipole focus) high xF = xbeam – xtarget • Valence Beam quarks at high-x. • Sea-target quarks at low/intermediate-x. • Next-to-leading order diagrams complicate the picture and must be considered • These diagrams are responsible for 50% of the measured cross section • Intrinsic transverse momentum of quarks (although a small effect, l > 0.8) Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  10. Pion Drell-Yan Data: Fermilab E615 Fermilab E615 • 252 GeV π-W Drell-Yan • Projected each data point onto xπ axis (diagonal) • Valence quark distributions extracted assuming xq(x) = A xα(1-x)β Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  11. Pion Drell-Yan Data: CERN NA3 (p§) NA10 (p-) NA3200 GeV p-data (also have 150 and 180 GeV p- and 200 GeV p+data). Can determine pion sea! NA10194 GeV p-data Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  12. 1 1 QCD Evolution xqvp(x,q) qvp(x,q0) 0 0 1 1 0 0 x x Models of the Pion At some base Q0 pQCD: xq(x)/ (1-x)bb = 2 NJL: xq(x)/ (1-x)bb = 1 DSE: xq(x)/ (1-x)bb¼ 1.9 Evolution to experimental Q increases b. • Data favor linear slope at high-xBj • Remember what was measured Structurelesspion described by old parameterization with a =0.67, b =1.13 (NJL Model) Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  13. Could it be a problem with the treatment of the raw data? • More flexible parameterization (Hecht et al.) • Modern ProtonPDF w/nuclear corrections • Inclusion of NLO terms rather than K-Factor • Look at 800 GeV proton-proton Drell-Yan: • Higher twist terms? Proton-proton K-factor is not constant at high xF (high xp)! Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  14. Fit of Drell-Yan Data in NLO • Sea quark parameterization from fits to π+/π- Drell-Yan data • Number of valence quarks [defines normalization on qpv(x)]: • Total momentum conservation: • Gluon content determined from other data (NA3/10 and WA80 direct photon) Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  15. Conway fit New fit to sDY data (not to these points) What did we learn? • Even with new freedom from parameterization, curve does not change. • Weak higher twist effects. • Data do NOT prefer convex-up shape at high-xp as required by DSE analysis! • But this is not the end of the story! Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  16. Soft Gluon Resummation • ωabis hard scattering function • Resum large logarithmic “soft” gluon contributions which arise as • Accomplished with combined Mellin and Fourier transform of the cross section Aicher, Schäfer and Vogelsang, arXiv:1009.2481 • Refit of pion Drell-Yan data Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  17. Soft Gluon Resummation β = 2.03 ±0.06 QCD and Dyson-Schwinger survive! pQCD: xq(x)/ (1-x)bb = 2 DSE: xq(x)/ (1-x)bb¼ 1.9 Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  18. K/π Drell-Yan Ratios More recent developments: • Predictions of the K/p Drell-Yan ratio based on Bethe-Salpeter Equations (BSE) • Can we get a Kaon beam to test this high-xBj structure of the Kaon? A. Bashir, T. Nguyen, C.D. Roberts and P.C. Tandy, in preparation Data: Badieret al. Phys. Lett. B93 354 (1980) Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  19. Conclusions • Large xBj structure of the pion is interesting and relevant • Pion cloud & antiquark flavor asymmetry • Nuclear Binding • Simple QCD state & Goldstone Boson • Even with NLO fit and modern parton distributions, pion did not agree with pQCD and Dyson-Schwinger • Soft Gluon Resummation saves the day! • What does this mean for other large-xBj Drell-Yan data? • Additional Bethe-Salpeter predictions to check in π/K Drell-Yan ratio Aicher, Schäfer and Vogelsang, arXiv:1009.2481 This work is supported in part by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC02-06CH11357. Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  20. Backup Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  21. Good Fit? Residuals Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  22. Look at 800 GeV proton-proton Drell-Yan: Proton-proton K-factor is not constant at high xF (high xp)! Caveat: The K factor • K factor relates Leading Order to Next-to-Leading order cross section calculations: sexp¼sNLO¼ = K sLO where K¼ 2 • Taken to be a constant independent of kinematics—Is it? • Possibly NLO analysis will show DSE behavior. • NLO fit can be done—remember this is “work in progress”—but at the cost of computer time. Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  23. xp resolution Caveat: xp Resolution J/y Best case, xp and xN contribute equally (E866 experience Dxp= 5 DxN)Dxp/xp¼ 0.14) xp resolution not quoted in paper or thesis Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  24. Caveat: xp Resolution (cont.) J/y Resolution misrepresentation arises from projecting into xp-xN space. Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

  25. Drell-Yan Polarization & Higher Twist • High xp show higher twist—Berger and Brodsky: • ds/ (1-xp)2[1+cos2(q)] • + 4/9 xphkT2isin2(q) / m2 • Drell-Yan is transversly polarized: ds/ 1+l cos2(q) Include higher twist term in parameterization! Paul E. Reimer, 3rd International Workshop on Nucleon Structure at Large Bjorken x

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